High-order accurate multi-sub-step implicit integration algorithms with dissipation control for hyperbolic problems

This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge–Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step, and thus, the trapezoidal rule is always employed in the first sub-step. This...

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Vydáno v:Archive of applied mechanics (1991) Ročník 94; číslo 8; s. 2285 - 2334
Hlavní autoři: Li, Jinze, Li, Hua, Yu, Kaiping, Zhao, Rui
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2024
Springer Nature B.V
Témata:
Accuracy
Algorithms
Classical Mechanics
Dissipation
Engineering
Forced vibration
Implicit methods
Load
Original
Runge-Kutta method
Stiffness matrix
Theoretical and Applied Mechanics
Velocity
Optimal spectral features
Dissipation control
High-order accuracy
ESDIRK
Implicit time integration
ISSN:0939-1533, 1432-0681
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Shrnutí:This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge–Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step, and thus, the trapezoidal rule is always employed in the first sub-step. This paper demonstrates for the first time that the proposed s -sub-step implicit method with s ≤ 6 can reach s th-order accuracy when achieving dissipation control and unconditional stability simultaneously. Hence, this paper develops, analyzes, and compares four cost-optimal high-order implicit algorithms within the present s -sub-step method using three, four, five, and six sub-steps. Each high-order implicit algorithm shares identical effective stiffness matrices to achieve optimal spectral properties. Unlike the published algorithms, the proposed high-order methods do not suffer from the order reduction for solving forced vibrations. Moreover, the novel methods overcome the defect that the authors’ previous algorithms require an additional solution to obtain accurate accelerations. Linear and nonlinear examples are solved to confirm the numerical performance and superiority of four novel high-order algorithms.
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ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-024-02637-y